Accurate Autism Spectrum Disorder (ASD) diagnosis is vital for early intervention. This study presents a hybrid deep learning framework combining Vision Transformers (ViT) and Vision Mamba to detect ASD using eye-tracking data. The model uses attention-based fusion to integrate visual, speech, and facial cues, capturing both spatial and temporal dynamics. Unlike traditional handcrafted methods, it applies state-of-the-art deep learning and explainable AI techniques to enhance diagnostic accuracy and transparency. Tested on the Saliency4ASD dataset, the proposed ViT-Mamba model outperformed existing methods, achieving 0.96 accuracy, 0.95 F1-score, 0.97 sensitivity, and 0.94 specificity. These findings show the model's promise for scalable, interpretable ASD screening, especially in resource-constrained or remote clinical settings where access to expert diagnosis is limited.